Planning multi-contact motions in a receding horizon fashion requires a value function to guide the planning with respect to the future, e.g., building momentum to traverse large obstacles. Traditionally, the value function is approximated by computing trajectories in a prediction horizon (never executed) that foresees the future beyond the execution horizon. However, given the non-convex dynamics of multi-contact motions, this approach is computationally expensive. To enable online Receding Horizon Planning (RHP) of multi-contact motions, we find efficient approximations of the value function. Specifically, we propose a trajectory-based and a learning-based approach. In the former, namely RHP with Multiple Levels of Model Fidelity, we approximate the value function by computing the prediction horizon with a convex relaxed model. In the latter, namely Locally-Guided RHP, we learn an oracle to predict local objectives for locomotion tasks, and we use these local objectives to construct local value functions for guiding a short-horizon RHP. We evaluate both approaches in simulation by planning centroidal trajectories of a humanoid robot walking on moderate slopes, and on large slopes where the robot cannot maintain static balance. Our results show that locally-guided RHP achieves the best computation efficiency (95%-98.6% cycles converge online). This computation advantage enables us to demonstrate online receding horizon planning of our real-world humanoid robot Talos walking in dynamic environments that change on-the-fly.

This work presents a novel RGB-D-inertial dynamic SLAM method that can enable accurate localisation when the majority of the camera view is occluded by multiple dynamic objects over a long period of time. Most dynamic SLAM approaches either remove dynamic objects as outliers when they account for a minor proportion of the visual input, or detect dynamic objects using semantic segmentation before camera tracking. Therefore, dynamic objects that cause large occlusions are difficult to detect without prior information. The remaining visual information from the static background is also not enough to support localisation when large occlusion lasts for a long period. To overcome these problems, our framework presents a robust visual-inertial bundle adjustment that simultaneously tracks camera, estimates cluster-wise dense segmentation of dynamic objects and maintains a static sparse map by combining dense and sparse features. The experiment results demonstrate that our method achieves promising localisation and object segmentation performance compared to other state-of-the-art methods in the scenario of long-term large occlusion.

State-of-the-art approaches to footstep planning assume reduced-order dynamics when solving the combinatorial problem of selecting contact surfaces in real time. However, in exchange for computational efficiency, these approaches ignore joint torque limits and limb dynamics. In this work, we address these limitations by presenting a topology-based approach that enables model predictive control (MPC) to simultaneously plan full-body motions, torque commands, footstep placements, and contact surfaces in real time. To determine if a robot's foot is inside a contact surface, we borrow the winding number concept from topology. We then use this winding number and potential field to create a contact-surface penalty function. By using this penalty function, MPC can select a contact surface from all candidate surfaces in the vicinity and determine footstep placements within it. We demonstrate the benefits of our approach by showing the impact of considering full-body dynamics, which includes joint torque limits and limb dynamics, on the selection of footstep placements and contact surfaces. Furthermore, we validate the feasibility of deploying our topology-based approach in an MPC scheme and explore its potential capabilities through a series of experimental and simulation trials.

Deployment of robotic systems in the real world requires a certain level of robustness in order to deal with uncertainty factors, such as mismatches in the dynamics model, noise in sensor readings, and communication delays. Some approaches tackle these issues reactively at the control stage. However, regardless of the controller, online motion execution can only be as robust as the system capabilities allow at any given state. This is why it is important to have good motion plans to begin with, where robustness is considered proactively. To this end, we propose a metric (derived from first principles) for representing robustness against external disturbances. We then use this metric within our trajectory optimization framework for solving complex loco-manipulation tasks. Through our experiments, we show that trajectories generated using our approach can resist a greater range of forces originating from any possible direction. By using our method, we can compute trajectories that solve tasks as effectively as before, with the added benefit of being able to counteract stronger disturbances in worst-case scenarios.

We present a versatile framework for the computational co-design of legged robots and dynamic maneuvers. Current state-of-the-art approaches are typically based on random sampling or concurrent optimization. We propose a novel bilevel optimization approach that exploits the derivatives of the motion planning sub-problem (i.e., the lower level). These motion-planning derivatives allow us to incorporate arbitrary design constraints and costs in an general-purpose nonlinear program (i.e., the upper level). Our approach allows for the use of any differentiable motion planner in the lower level and also allows for an upper level that captures arbitrary design constraints and costs. It efficiently optimizes the robot's morphology, payload distribution and actuator parameters while considering its full dynamics, joint limits and physical constraints such as friction cones. We demonstrate these capabilities by designing quadruped robots that jump and trot. We show that our method is able to design a more energy-efficient Solo robot for these tasks.

This work presents an approach for modelling and tracking previously unseen objects for robotic grasping tasks. Using the motion of objects in a scene, our approach segments rigid entities from the scene and continuously tracks them to create a dense and sparse model of the object and the environment. While the dense tracking enables interaction with these models, the sparse tracking makes this robust against fast movements and allows to redetect already modelled objects. The evaluation on a dual-arm grasping task demonstrates that our approach 1) enables a robot to detect new objects online without a prior model and to grasp these objects using only a simple parameterisable geometric representation, and 2) is much more robust compared to the state of the art methods.

Robot design optimization, imitation learning and system identification share a common problem which requires optimization over robot or task parameters at the same time as optimizing the robot motion. To solve these problems, we can use differentiable optimal control for which the gradients of the robot's motion with respect to the parameters are required. We propose a method to efficiently compute these gradients analytically via the differential dynamic programming (DDP) algorithm using sensitivity analysis (SA). We show that we must include second-order dynamics terms when computing the gradients. However, we do not need to include them when computing the motion. We validate our approach on the pendulum and double pendulum systems. Furthermore, we compare against using the derivatives of the iterative linear quadratic regulator (iLQR), which ignores these second-order terms everywhere, on a co-design task for the Kinova arm, where we optimize the link lengths of the robot for a target reaching task. We show that optimizing using iLQR gradients diverges as ignoring the second-order dynamics affects the computation of the derivatives. Instead, optimizing using DDP gradients converges to the same optimum for a range of initial designs allowing our formulation to scale to complex systems.

This work presents a novel dense RGB-D SLAM approach for dynamic planar environments that enables simultaneous multi-object tracking, camera localisation and background reconstruction. Previous dynamic SLAM methods either rely on semantic segmentation to directly detect dynamic objects; or assume that dynamic objects occupy a smaller proportion of the camera view than the static background and can, therefore, be removed as outliers. Our approach, however, enables dense SLAM when the camera view is largely occluded by multiple dynamic objects with the aid of camera motion prior. The dynamic planar objects are separated by their different rigid motions and tracked independently. The remaining dynamic non-planar areas are removed as outliers and not mapped into the background. The evaluation demonstrates that our approach outperforms the state-of-the-art methods in terms of localisation, mapping, dynamic segmentation and object tracking. We also demonstrate its robustness to large drift in the camera motion prior.

Benchmarks of state-of-the-art rigid-body dynamics libraries report better performance solving the inverse dynamics problem than the forward alternative. Those benchmarks encouraged us to question whether that computational advantage would translate to direct transcription, where calculating rigid-body dynamics and their derivatives accounts for a significant share of computation time. In this work, we implement an optimization framework where both approaches for enforcing the system dynamics are available. We evaluate the performance of each approach for systems of varying complexity, for domains with rigid contacts. Our tests reveal that formulations using inverse dynamics converge faster, require less iterations, and are more robust to coarse problem discretization. These results indicate that inverse dynamics should be preferred to enforce the nonlinear system dynamics in simultaneous methods, such as direct transcription.

Path planning and collision avoidance are challenging in complex and highly variable environments due to the limited horizon of events. In literature, there are multiple model- and learning-based approaches that require significant computational resources to be effectively deployed and they may have limited generality. We propose a planning algorithm based on a globally stable passive controller that can plan smooth trajectories using limited computational resources in challenging environmental conditions. The architecture combines the recently proposed fractal impedance controller with elastic bands and regions of finite time invariance. As the method is based on an impedance controller, it can also be used directly as a force/torque controller. We validated our method in simulation to analyse the ability of interactive navigation in challenging concave domains via the issuing of via-points, and its robustness to low bandwidth feedback. A swarm simulation using 11 agents validated the scalability of the proposed method. We have performed hardware experiments on a holonomic wheeled platform validating smoothness and robustness of interaction with dynamic agents (i.e., humans and robots). The computational complexity of the proposed local planner enables deployment with low-power micro-controllers lowering the energy consumption compared to other methods that rely upon numeric optimisation.

This work presents a novel RGB-D SLAM approach to simultaneously segment, track and reconstruct the static background and large dynamic rigid objects that can occlude major portions of the camera view. Previous approaches treat dynamic parts of a scene as outliers and are thus limited to a small amount of changes in the scene, or rely on prior information for all objects in the scene to enable robust camera tracking. Here, we propose to treat all dynamic parts as one rigid body and simultaneously segment and track both static and dynamic components. We, therefore, enable simultaneous localisation and reconstruction of both the static background and rigid dynamic components in environments where dynamic objects cause large occlusion. We evaluate our approach on multiple challenging scenes with large dynamic occlusion. The evaluation demonstrates that our approach achieves better motion segmentation, localisation and mapping without requiring prior knowledge of the dynamic object's shape and appearance.

Shooting methods are an efficient approach to solving nonlinear optimal control problems. As they use local optimization, they exhibit favorable convergence when initialized with a good warm-start but may not converge at all if provided with a poor initial guess. Recent work has focused on providing an initial guess from a learned model trained on samples generated during an offline exploration of the problem space. However, in practice, the solutions contain discontinuities introduced by system dynamics or the environment. Additionally, in many cases, multiple equally suitable, i.e., multimodal, solutions exist to solve a problem. Classic learning approaches smooth across the boundary of these discontinuities and thus generalize poorly. In this work, we apply tools from algebraic topology to extract information on the underlying structure of the solution space. In particular, we introduce a method based on persistent homology to automatically cluster the dataset of precomputed solutions to obtain different candidate initial guesses. We then train a mixture-of-experts within each cluster to predict state and control trajectories to warm-start the optimal control solver and provide a comparison with modality-agnostic learning. We demonstrate our method on a cartpole toy problem and a quadrotor avoiding obstacles, and show that clustering samples based on inherent structure improves the warm-start quality.

Optimal control is a popular approach to synthesize highly dynamic motion. Commonly, L-2 regularization is used on the control inputs in order to minimize energy used and to ensure smoothness of the control inputs. However, for some systems, such as satellites, the control needs to be applied in sparse bursts due to how the propulsion system operates. In this paper, we study approaches to induce sparsity in optimal control solutions-namely via smooth L-1 and Huber regularization penalties. We apply these loss terms to state-of-the-art Differential Dynamic Programming (DDP)-based solvers to create a family of sparsity-inducing optimal control methods. We analyze and compare the effect of the different losses on inducing sparsity, their numerical conditioning, their impact on convergence, and discuss hyperparameter settings. We demonstrate our method in simulation and hardware experiments on canonical dynamics systems, control of satellites, and the NASA Valkyrie humanoid robot. We provide an implementation of our method and all examples for reproducibility on GitHub.

This paper focuses on robustness to disturbance forces and uncertain payloads. We present a novel formulation to optimize the robustness of dynamic trajectories. A straightforward transcription of this formulation into a nonlinear programming problem is not tractable for state-of-the-art solvers, but it is possible to overcome this complication by exploiting the structure induced by the kinematics of the robot. The non-trivial transcription proposed allows trajectory optimization frameworks to converge to highly robust dynamic solutions. We demonstrate the results of our approach using a quadruped robot equipped with a manipulator.

In this paper, we study a wheeled robot with a prismatic extension joint. This allows the robot to build up momentum to perform jumps over obstacles and to swing up to the upright position after the loss of balance. We propose a template model for the class of such two-wheeled jumping robots. This model can be considered as the simplest wheeled-legged system. We provide an analytical derivation of the system dynamics which we use inside a model predictive controller (MPC). We study the behavior of the model and demonstrate highly dynamic motions such as swing-up and jumping. Furthermore, these motions are discovered through optimization from first principles. We evaluate the controller on a variety of tasks and uneven terrains in a simulator.

The goal of this paper is to improve our previous Dynamic Obstacle Mapping (DOMap) system by means of improving the perception stage. The new system must deal with robots and people as dynamic obstacles using LIght Detection And Range (LIDAR) sensor in order to collect the surrounding information. Although robot movement can be easily tracked by an Extended Kalman Filter (EKF), people’s movement is more unpredictable and it might not be correctly linearized by an EKF. Therefore, to deal with a better estimation of both types of dynamic objects in the local map it is recommended to improve our previous work. The DOMap has been extended in three key points: first the LIDAR reflectivity remission is used to make more robust the matching in the optical flow of the detection stage, secondly static and a dynamic occlusion detectors have been proposed, and finally a tracking stage based on Particle Filter (PF) has been used to deal with robots and people as dynamic obstacles. Therefore, our new improved-DOMap (iDOMap) provides maps with information about occupancy and velocities of the surrounding dynamic obstacles (robots, people, etc.) in a more robust way and they are available to improve the following planning stage.

Common formulations to consider collision avoidance in trajectory optimization often use either preprocessed environments or only check and penalize collisions at discrete time steps. However, when only checking at discrete states, this requires either large margins that prevent manipulation close to obstacles or dense time discretization increasing the dimensionality of the optimization problem in complex environments. Nonetheless, collisions may still occur in the interpolation/transition between two valid states or in environments with thin obstacles. In this work, we introduce a computationally inexpensive continuous-time collision avoidance term in presence of static and moving obstacles. Our penalty is based on conservative advancement and harmonic potential fields and can be used as either a cost or constraint in off-the-shelf non-linear programming solvers. Due to the use of conservative advancement (collision checks) rather than distance computations, our method outperforms discrete collision avoidance based on signed distance constraints resulting in smooth motions with continuous-time safety while planning in discrete time. We evaluate our proposed continuous collision avoidance on scenarios including manipulation of moving targets, locomanipulation on mobile robots, manipulation trajectories for humanoids, and quadrotor path planning and compare penalty terms based on harmonic potential fields with ones derived from contact normals.

While widely studied in robotics for decades, mobile manipulation has recently seen a surge in interest for industrial applications due to increasing demands on flexibility and agility alongside productivity, particularly in small and medium enterprises. However, most mobile manipulation solutions frequently decouple the navigation from the manipulation problem effectively performing fixed-base manipulation using a repositionable manipulator. This is not only inefficient, but moreover limits the range of applications and disregards the inherent redundancy of a mobile manipulation system. In this work, we introduce a high-performance omnidirectional mobile manipulation platform with integrated whole-body control, real-time collision-free whole-body motion planning, and perception. We demonstrate its capability along with application scenarios on technical demonstrators involving moving manipulation targets as well as whole-body manipulation in simulation and hardware experiments. Finally, we deploy and evaluate our solution in field trials on an industrial oil and gas training facility on a sensor placement and manipulation task.

In this work we present an articulated tracking approach for robotic manipulators, which relies only on visual cues from colour and depth images to estimate the robot's state when interacting with or being occluded by its environment. We hypothesise that articulated model fitting approaches can only achieve accurate tracking if subpixel-level accurate correspondences between observed and estimated state can be established. Previous work in this area has exclusively relied on either discriminative depth information or colour edge correspondences as tracking objective and required initialisation from joint encoders. In this paper we propose a coarse-to-fine articulated state estimator, which relies only on visual cues from colour edges and learned depth keypoints, and which is initialised from a robot state distribution predicted from a depth image. We evaluate our approach on four RGB-D sequences showing a KUICA LWR arm with a Schunk SDH2 hand interacting with its environment and demonstrate that this combined keypoint and edge tracking objective can estimate the palm position with an average error of 2. 5cm without using any joint encoder sensing.

In this letter, we first theoretically prove the conditions and boundaries of resolution completeness for deterministic roadmap methods with a discretized workspace. A novel variant of such methods, the hierarchical dynamic roadmap (HDRM), is then proposed for solving complex planning problems. A unique hierarchical structure to efficiently encode the configuration-to-workspace occupation information is introduced and allows the robot to check the collision state of tens of millions of samples on-the-fly-the number of which was previously strictly limited by available memory. The hierarchical structure also significantly reduces the time for path searching, hence, the robot is able to find feasible motion plans in real-time in extremely constrained environments. A rigorous benchmarking shows that HDRM is robust and computationally fast compared with classical dynamic roadmap methods and other state-of-the-art planning algorithms. Experiments on the seven degree-of-freedom KUKA LWR robotic arm integrated with live perception further validate the effectiveness of HDRM in complex environments.